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Free Percentage Calculator Online

Percentage calculator

Six everyday percentage questions, each written as a sentence you fill in. Every answer shows the working, so you can check it, or learn to do it yourself.

percentPercent of a numbertip, tax, share

What is%of%?

1215 ÷ 100 × 80 = 12content_copy

functionsWhat percent is X of Yscore, share, progress

%is what % of%?

25%45 ÷ 180 × 100 = 25%content_copy

trending_upPercentage changeprice rise, growth

From%to%

+25% increase(100 − 80) ÷ 80 × 100 = 25%content_copy

add_circleIncrease by a percentadd VAT, a raise

Add%to%

6050 × (1 + 20 ÷ 100) = 60content_copy

sellDecrease by a percentdiscount, sale price

Take%off%

66.7589 × (1 − 25 ÷ 100) = 66.75content_copy

historyOriginal before a percentprice before tax

%after adding%

100120 ÷ (1 + 20 ÷ 100) = 100content_copy

~/in-your-head

Four tricks to do percentages without a calculator.

10%Move the decimalTen percent is always the number with the decimal point moved one place left.10% of 240 = 24.0

5%Half of tenFind 10%, then halve it. Great for tips and small discounts.10% of 60 = 65% of 60 = 3

x%Flip it roundx% of y is the same as y% of x: pick whichever is easier.8% of 50= 50% of 8 = 4

1%Build from 1%Find 1% (÷ 100), then multiply up to any percentage.1% of 350 = 3.57% = 24.5

~/where-people-go-wrong

Three percentage traps.

Up then down isn’t even

closeA price up 50% then down 50% is back where it started.

checkIt ends 25% lower: 100 → 150 → 75.

The second percentage is taken of a bigger number, so it removes more than the first one added.

Points vs percent

closeInterest rising from 2% to 3% is a 1% increase.

checkIt’s 1 percentage point, but a 50% increase.

“Percentage points” measure the gap between two rates; “percent” measures relative change.

Removing tax

closeRemove 20% VAT from 120 by taking 20% off: 96.

checkDivide by 1.2 instead: 100.

The 20% was added to the original, so it must be removed from the original too: use “Original before a percent”.

~/measuring-change

One change, six ways to report it.

“Up 25%” and “down 20%” describe the same gap between 80 and 100. Pick two values and see every standard way of expressing the change, and where each one breaks.

From (the base)To

to ÷ from = ×1.25 · from ÷ to = ×0.8

warning

Percent change(to − from) ÷ from × 100The standard figure. Its size depends on which end you call the base.

+25%

Reverse percent change(from − to) ÷ to × 100The same gap read backwards. Not simply the negative of the first.

-20%

Change vs |base|(to − from) ÷ |from| × 100Keeps the sign honest when the starting value is negative, such as a loss turning into a profit.

+25%

Symmetric (midpoint) change(to − from) ÷ ((from + to) ÷ 2) × 100Same size in both directions; used for arc elasticity in economics. Bounded at ±200% for positive values.

+22.2222%

Log change100 × ln(to ÷ from)Symmetric and additive: the log changes in a chain simply add up. Needs both values positive.

+22.3144 log pts

Absolute differenceto − fromIf both values are rates, this is the change in percentage points.

+20

Chained changes don’t add upType a run of percentage changes. Each one applies to the result of the last, so they multiply.

100+50%arrow_forward150-50%arrow_forward75

Actual total change-25%Factors multiply: ×1.5 ×0.5 = ×0.75

Sum of the steps0%What gets reported by mistake. Only close when every change is small.

Arithmetic mean step0%Repeated 2 times this gives 0%, not the actual result.

Geometric mean step-13.3975%The single rate that, repeated 2 times, lands exactly on the result, the idea behind CAGR.

The recovery gapAfter a fall of L%, getting back needs a rise of L ÷ (100 − L) × 100.

−50% needs +100%100 → 50 → back to 100 = ×2

−10%

+11.1%

−20%

+25%

−30%

+42.9%

−40%

+66.7%

−50%

+100%

−60%

+150%

−70%

+233.3%

−80%

+400%

−90%

+900%

~/rounded-percentages

Why 33 + 33 + 33 = 99, and what rounded figures give away.

Rounding each share on its own can leave a total of 99 or 101. Run the other way, rounded percentages leak information: only certain sample sizes can produce them.

Counts → percentages

GroupExactRound eachTruncateLargest remainder

A · 228.571%29%28%29%

B · 228.571%29%28%28%

C · 342.857%43%42%43%

Total100%101%98%100%

Largest remainder (Hare) truncates every share, then hands the missing units to the shares with the biggest leftover fractions: highlighted in orange. The total is always exactly 100, at the price of rounding some shares the “wrong” way.

Percentages → smallest possible sample

Claimed N

Smallest N = 31/3 = 33.33% · 2/3 = 66.67%

61 of the sample sizes from 1 to 100 are consistent

36912151821242730333639404243454648495152545557586061636466676970727375767879+21 more

A share shown to d decimals could be anything within ±half a unit of the last digit. For each N the page finds the whole counts that fit every share, and whether they can add up to N. The same idea, applied to reported averages, is the GRIM test used to spot impossible statistics in published papers.

~/when-percentages-mislead

Better in every group, worse overall.

A pooled percentage is a weighted average, and the weights can do the talking. Below: real kidney-stone outcomes from a 1986 BMJ study, and the gap between relative and absolute risk.

Success rate by treatment

Treatment A (open surgery)Treatment B (PCNL)

Small stones (< 2 cm)

93.1%

86.7%

Large stones (≥ 2 cm)

73.0%

68.8%

All patients

273 / 35078.0%

289 / 35082.6%

Case mix: share of each treatment’s patients in the harder group

A · large

75%

B · large

23%

swap_vertReversal: A has the higher success rate for both small and large stones, yet B wins overall (82.6% vs 78.0%). A was given mostly to large stones (75% of its patients), which fail more often whatever the treatment. Pooling hides that confounder.

Relative vs absolute risk“Doubles the risk” means very different things for a 1-in-7,000 risk and a 1-in-5 risk.

Baseline risk %Relative change %

Before

After

Headline“Raises risk by 50%”

Absolute change+1 percentage points

Per 10,000 people200 → 300 cases (+100)

Number needed to harm1 extra case for every 100 people

~/reference

Signs, units and formats.

How 12.5% is written around the world, formatted live by your browser, plus the smaller-than-percent units and which tools multiply by 100 for you.

LocaleOutputSignNon-digit characters

English (US)en-US12.5%afterU+002E full stop · U+0025 percent sign

Germande-DE12,5 %afterU+002C comma · U+00A0 no-break space · U+0025 percent sign

Frenchfr-FR12,5 %afterU+002C comma · U+00A0 no-break space · U+0025 percent sign

Swedishsv-SE12,5 %afterU+002C comma · U+00A0 no-break space · U+0025 percent sign

Turkishtr-TR%12,5beforeU+0025 percent sign · U+002C comma

Basqueeu-ES12.5%afterU+002E full stop · U+0025 percent sign

Hebrewhe-IL12.5%afterU+002E full stop · U+0025 percent sign

Arabic (Egypt)ar-EG١٢٫٥٪؜afterU+066B arabic decimal separator · U+066A arabic percent sign · U+061C arabic letter mark

Persianfa-IR۱۲٫۵٪afterU+066B arabic decimal separator · U+066A arabic percent sign

Japaneseja-JP12.5%afterU+002E full stop · U+0025 percent sign

new Intl.NumberFormat(locale, { style: 'percent', maximumFractionDigits: 1 }).format(0.125), results come from your browser’s CLDR data and can differ between browsers and versions.

Smaller than a percent%

Percent% U+00251 / 1000.25 %

Per mille‰ U+20301 / 1,0002.5 ‰

Basis pointbp · ‱ U+20311 / 10,00025 bp

Per cent millepcm1 / 100,000250 pcm

Parts per millionppm1 / 10⁶2,500 ppm

Parts per billionppb1 / 10⁹2,500,000 ppb

The SI Brochure accepts % (with a space before it) but discourages ppm, ppb and ppt, since “billion” and “trillion” mean different powers of ten in different languages.

Who multiplies by 100 for you?

JavaScript IntlIntl.NumberFormat('en-US',{style:'percent'}).format(0.05) → "5%" (live)yes

Python'{:.0%}'.format(0.05) → '5%'yes

Excel / Sheetstyping 5% stores 0.05; % format on 5 shows 500%yes

CSSwidth: 5% → 5% of the containing blockno

C printfprintf("%d%%", 5) → 5% (%% is a literal %)no

SQLFORMAT(0.05, 'P') in SQL Server (en-US) → 5.00%yes

Timeline

c. AD 6Augustus introduces the centesima rerum venalium, a tax of one hundredth on goods sold at auction.

1400sItalian merchant arithmetic writes “per cento”, abbreviated in manuscripts to forms like “p cento” and “p c°”.

1600sThe abbreviation shrinks to “per o/o”; the “per” is later dropped, leaving the o/o shape that becomes %.

1903Udny Yule describes how pooled association can differ from association within groups.

1951Edward Simpson publishes the reversal example that later carries his name.

1963ASCII assigns % to code 0x25; Unicode keeps it as U+0025.

1985Törnqvist, Vartia and Vartia argue the log change is the best measure of relative change.

1986Charig et al. publish the kidney-stone comparison now used to teach Simpson’s paradox.

1991Unicode 1.0 includes the per mille sign ‰ (U+2030).

2012ECMA-402 1st edition adds Intl.NumberFormat with style “percent”, which multiplies by 100.

2016Brown and Heathers publish the GRIM test for impossible reported means.

2019SI Brochure 9th edition: % is accepted for 0.01, written with a space before it.

Dates before 1900 are approximate and come from general histories of notation; check primary sources before citing.

Sources

BIPM, The International System of Units (SI Brochure, 9th ed.)Rules for %, ppm and dimensionless quantities.Unicode: General Punctuation chartU+2030 per mille and U+2031 per ten thousand.ECMA-402: Internationalization APIIntl.NumberFormat and the percent style.Simpson (1951), J. R. Stat. Soc. B 13(2)The interpretation of interaction in contingency tables.Charig et al. (1986), BMJ 292Comparison of treatment of renal calculi, the kidney-stone data.Törnqvist, Vartia & Vartia (1985), The American Statistician 39(1)How should relative changes be measured?Brown & Heathers (2016), Soc. Psychol. Personal. Sci.The GRIM test: detecting impossible reported means.Unicode: Basic Latin chartU+0025 percent sign, inherited from ASCII.

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